Gabbie Gonzalez‘s father, Francisco Gonzalez — an injury attorney — may face punishment by the Florida Bar Association … which opened a disciplinary file after he was charged with conspiring to have singer Jack Avery murdered.

A spokesperson for the Florida Bar tells TMZ … “We can confirm that a discipline file has been opened on this matter” — this after Gonzalez was hit with the criminal charge in Los Angeles County.

This begins a process which could lead to potential discipline down the road, including possibly disbarment … though it could also end without any punishment should the review board decide punishment is unnecessary.

As you know … Gabbie and Francisco were arrested Tuesday and charged with conspiracy to commit murder. Prosecutors claim they collaborated on a plot to kill Gabbie’s ex — and the father of her child — Avery.

Gabbie and Jack were engaged in a custody battle over their 7-year-old daughter … and Francisco allegedly told her it’d be cheaper to simply kill Jack than battle this one out in court. Authorities allege Francisco sent Gabbie’s friend Kai Cordrey $10K to pay for a hit man to take out Jack.

According to court documents, investigators say Gabbie and Kai discussed possibly making Jack’s murder look like a car accident.