Many bar members were troubled to learn of possible shortfalls in the client accounts of the late New Haven lawyer William Gallagher. And now it appears that there will be no easy resolution of the situation.

Complications arose this month when an attorney who worked for Gallagher filed a motion in court seeking $35,000 in fees she claims are owed to her. The request by attorney Barbara Cox through her lawyer, William Clendenen, is the first of what could be many potential claims for payment from Gallagher’s accounts.

Patricia King, the state’s Chief Disciplinary Counsel, could not say how many other people she expects will come forward with claims. “It’s going to take some time” to complete a review of Gallagher’s accounts, King said.

Cox says she who worked as a salaried associate for Gallagher’s firm for nearly 19 years, from March 1991 to February 2010. Afterward, she worked as an independent contractor for Gallagher until his death on Dec. 26, 2013.

In the motion Cox filed, she argues that if client funds are missing from her former boss’s IOLTA accounts, that has nothing to do with her.

“It is respectfully submitted that it is unfair to penalize Cox for any wrongdoing by Gallagher or the firm in respect to clients funds accounts,” Clendenen wrote in the motion, which seeks payment for his client. “At no time was Cox ever a signatory to the firm’s clients’ funds accounts, nor did she have any authority to transact any business in those accounts. She had no knowledge or involvement in any transaction in those accounts.”

Beyond denying any knowledge of financial improprieties, Cox claims Gallagher owed her money. In March 2012, Familymeds, an online pharmacy based in Farmington, retained the Gallagher firm to represent it as plaintiffs in a malpractice complaint against another law firm.

Cox says in her motion that she handled most aspects of that case, which eventually settled out of court for $600,000. Cox’s work for Familymeds included “analyzing the legal and factual issues, drafting the complaint, calculating damages, preparing a demand letter, negotiating a mediation agreement” and other document preparation, according to Cox’s motion.

Gallagher, in turn, negotiated an agreement with the defense counsel to allow the parties to resolve the case without a lawsuit being filed.

Based on her calculations, Cox billed for 141.5 hours of work on the case, while Gallagher billed 68.5 hours. Cox said she had an agreement with Gallagher to receive $225 an hour for her work. She wants to be paid when the firm is paid, according to Cox and Clendenen, neither of whom returned calls seeking comment.

Superior Court Judge Brian Fisher has scheduled a hearing on the matter June 23. If Fisher does not order payment, Cox has been told she may have to file a separate lawsuit against Gallagher’s estate.

A trustee who was appointed to wind down the firm’s finances, William Sweeney, has notified Gallagher’s former clients to come forward if they are owed money from the firm that was held in trust accounts. Fisher will hold a separate hearing on July 7, at which former clients will get a chance to present evidence of what they are owed from Gallagher’s trust accounts.