Is that allowed? Someone told me there may be a problem with it
Ask your Rav that you consult with on other matters.
In the past we did sign lease with a tenant right after Pesach which is sefira time.
Ask your Rav
This is definitely the only option. Dont take advice off anyone in a blog, even if they are a great talmid chochom and tremendous outstanding anav such as myself.
But I do believe you are confusing sefira with the 3 weeks where the aveilus is completely different. There is no problem in sefira eg to make shehechiyanu if you happen to come across a new food that you didnt set out to get. The halachos that we have are more to remind us of rabbi akiva’s talmidim and that these are special days of reflection. There are no issues of sakana or bad mazal in sefira.
Had it been considered proper aveilus, there would be no heter for someone to attend a chasuna during the half of sefira that they keep. But you ask your Rav.
My rav says that it would be better not to switch jobs or sign contracts during Sefiras haOmer because it is very much like the Three Weeks. Many tragedies have happened in the past to yidden during the Sefiras haOmer, and he does not believe that this is a good time to undertake new commitments. However, if you would face a substantial loss in not signing, then your Rav may counsel differently.