Hello Dmitrijs and welcome to our community!
Here4 is the Italian health ministry webpage listing entry requirements for Italy. It states:
From 1 May, regardless of the country of entry into Italy, the traveller will be required to present to the carrier and to whoever is in charge of checking:
- the COVID-19 Green Certificate13 or other equivalent certificate9 which must state one of the following conditions:
- completion of the primary vaccination series or booster dose according to the vaccination plans of the countries of release with vaccines authorized by the European Medical Agency (primary series validity 9 months and booster dose without predefined limit)
- recovery from SARS-CoV-2 infection (valid for 180 days from positive swab test)
- recovery after the administration of the first dose of vaccine or at the end of the primary vaccination series or following the administration of the relevant booster dose
- rapid antigen or molecular swab test, respectively within 48 or 72 hours before entry into Italy.
So, to answer your question, it depends on how long ago you completed your initial vaccination cycle as to whether the vaccination certificate is still valid for entry into Italy. If it was more than nine months ago, then you need to either get a booster or enter Italy with a negative result on a Covid test within the requirements listed in the last bullet point.
Hope this helps! Have a wonderful trip to Italy!