Yes, your client can issue a corrected 1099 for you. There's no deadline for a corrected 1099-NEC, but it's best to wait until the correction is filed before you file your tax return.
If your client refuses to change the 1099, you should prepare your tax return using the correct income amount as you normally would.
You may receive a letter from the IRS, send a response with proof (like bank statements, canceled checks, or invoices) to justify the income you reported.