When should i receive my tax forms for 2021?

If you mean your income reporting forms such as W-2 and 1099's, they should be sent to you by the end of January.

An employer said I should have received it by now, but I haven't. Can I pick up my 1099 from him or should I have him mail me another one? We moved recently, but were sure to forward our mail.

If you did not receive it then ask them for another one.   But they have until the end of January.   Make sure they have your new address.