In general, yes. Upon conviction criminal charges may be brought.
Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law.
Trump was impeached and acquitted for the acts he is being charged with criminally. That has never happened before, which is why the SCOTUS has taken up the case.
"The application for a stay presented to The Chief Justice
is referred by him to the Court. The Special Counsel’s request
to treat the stay application as a petition for a writ of
certiorari is granted, and that petition is granted limited to
the following question: Whether and if so to what extent does a
former President enjoy presidential immunity from criminal
prosecution for conduct alleged to involve official acts during
his tenure in office. Without expressing a view on the merits,
this Court directs the Court of Appeals to continue withholding
issuance of the mandate until the sending down of the judgment of
this Court. The application for a stay is dismissed as moot."