I have received my W2 for the year of 2021. I’m supposed to be waiting for a 1099 from a side gig I also did last year. Can I file that 1099 next year instead of waiting?

The 2021 Form 1099-NEC has to be reported on the 2021 tax return, Not on a future year tax return.

No. You must include the 1099 from your side gig for income earned in 2021 on your 2021 tax return. You can't wait and file it on the 2022 tax return. 

No. You have to report income in the year it was earned. 

No.  You have to report all your income each year.  They have until Jan 31 to send it to you.  Wait can't you wait?  Filing now won't get your refund any faster.

Actually you don't need to get or wait for the 1099NEC.  You can enter the amount without it.  You should be keeping your own good records of your income.

You can just enter it as Other self employment income or as Cash or General income.  You don't need to get a 1099NEC or 1099Misc or 1099K.  Even if you did you can enter all your income as Cash.  Only the total goes to schedule C.

How to enter income from Self Employment

https://ttlc.intuit.com/community/self-employed/help/how-do-i-report-income-from-self-employment/00/26653