The below explanation (English) has been kindly provided by Reddit user /u/Maksym_Kozub. The information below is in his own words, verbatim minus a few formatting edits for readability. The source of this information is located on /r/Ham Radio
On February 23, 2022, the President of Ukraine issued his Decree declaring the state of emergency for one month. By that Decree, the ban was indeed introduced. Then on February 24, after the full-scale invasion started, martial law was declared by another Presidential Decree, approved by the Verkhovna Rada (the Parliament of Ukraine) on the same day. Under martial law, the Cabinet of Ministers had to establish an action plan, which it did, but this time without any ban. However, the military command is authorized to introduce such ban, as well as other restrictions, either on its own or jointly with local/provincial Military Administrations etc.
The command, i.e. the General Staff, has not introduced it. Local/provincial administrations may have introduced it somewhere, but it is known for sure that at least in some provinces the ban was never introduced by their respective administrations. Some Ukrainian radio amateurs inquired about this matter and obtained direct “No ban” replies from local authorities. See e.g. https://v4l1k.notion.site/20-09-2022-6e81425f78124e89b7c0d4f0618ec163#162009851bfd4fb9b8a6fbefdb62f143 (in Ukrainian).
There, a Ukrainian radio amateur has published official replies he received. According to those, there is no ban in Chernihiv, Poltava, Vinnytsia, Kyiv, Lviv, Dnipropetrovsk, Khmelnytsky, Zaporizhzhia, Cherkasy, Kirovohrad, Kharkiv, and Zhytomyr oblasts (provinces).
To make it short: from March 26, if there is no local/regional ban, then there is no ban at all.
Issuance of new callsigns is a different thing. It does not work at the moment, but the reason is not the martial law as such. There has been some new legislation in Ukraine, effective from January 1, 2022, and the radio spectrum authorities etc. had to pass some technical/procedural regulations, to approve new forms of some documents, etc.
Those activities have not stopped, but slowed down for obvious reasons during the war. Sources (Ukrainian ham radio activists involved in those developments etc.) say that we can expect the renewal of callsign issuance in some 2-3 months.
P.S. I tend to monitor all those developments, because I am a Ukrainian who (1) has been planning to get a callsign and an amateur station, (2) is a former lawyer, and (3) joined the ranks voluntarily to defend my country in 2014, was seriously wounded near Luhansk on August 5, 2014, and returned to the trenches in 2015 after recovery.
Now, being almost 55, I am in the army again since May 20 (and again voluntarily).
I do not know the original poster, but I am writing here under my real name, which is quite well-known in Ukraine and not only in Ukraine. (For the last 28 years I have been one of the best-paid conference interpreters in Ukraine.) You are welcome to ask additional questions about the current regulatory situation regarding ham radio in Ukraine, if you have any.
Additional information has been supplied by the same poster for extra clarification and has been posted below verbatim.
Heroyam slava (Glory to heroes)! Thank you for your reply. By the way, Lubny is in Poltava Oblast (Province). The webpage I mentioned has, among other replies, the one from Poltava authorities. Here comes my quick translation of its full text for your understanding. I have purposely included the letterhead and all those bureaucratic formalities, in case your friend decides to contact those officials. Hope this helps.
POLTAVA OBLAST MILITARY ADMINISTRATION
DEPARTMENT FOR DEFENSE ACTIVITIES, CIVIL PROTECTION, AND INTERACTION WITH LAW ENFORCEMENT BODIES
14 Raisy Kyrychenko St, Poltava, 36039, tel./fax +380 532 50-04-24, +380 532 56-23-93
E-mail: email@example.com Web: uns.adm-pl.gov.ua Number in the Unified State Register of Enterprises and Organizations of Ukraine: 1437324
2022-06-29 No. 06-05/1038 In reply to No. KDL-1006 dated _
Municipal budget-funded Institution “Provincial Contact Center” of Poltava Provincial Council
Regarding provision of information
The Department for Defense Activities, Civil Protection, and Interaction with Law Enforcement Bodies of the Oblast Military Administration has thoroughly processed the inquiry No. KDL-1006, regarding provision of information about any restrictions introduced at the level of Poltava Oblast Military Administration with regard to operation of personal and collective amateur two-way radio stations. As a result of consideration, we hereby inform that through administrative documents of the Oblast Military Administration no decision was made on the introduction of any restrictions with regard to operation of personal and collective amateur two-way radio stations.
Director of the Department for Defense Activities, Civil Protection, and Interaction with Law Enforcement Bodies of the Oblast Military Administration (SIGNATURE) Viktor Steblianko
[Document prepared by:] Vitaliy Poteriayko, +380 532 56 53 60