The exact definition of Unlicensed Practice of Law (UPL) varies from state to state, and is often rather vague. Florida code section 454.23 provides that:
Any person not licensed or otherwise authorized to practice law in this state who practices law in this state or holds himself or herself out to the public as qualified to practice law in this state, or who willfully pretends to be, or willfully takes or uses any name, title, addition, or description implying that he or she is qualified, or recognized by law as qualified, to practice law in this state, commits a felony of the third degree.
But that does not clearly define "practice of law," nor does this page on UPL from the Florida bar.
In The Florida Bar v. Sperry, 140 So. 2d 587, 591 (Fla. 1962), the court wrote:
... if the giving of advice and performance of services affect important rights of a person under the law, and if the reasonable protection of the rights and property of those advised and served requires that the persons giving such advice possess legal skill and a knowledge of the law greater than that possessed by the average citizen, then the giving of such advice and the performance of such services by one for another as a course of conduct constitute the practice of law. (Quoted in "SUMMARY OF UNLICENSED PRACTICE OF LAW CASES" (PDF from the Florida courts)
The "Summary" (linked just above) further says:
Although a codified definition does not exist, there is a large body of case law applying the Sperry test to determine whether a specific activity constitutes the unlicensed practice of law. Therefore, although one cannot go to one particular source such as a dictionary for a definition, in most instances whether an activity constitutes the unlicensed practice of law can be found in case law.
An attorney admitted to the practice of law in a state other than Florida may not engage in the general practice of law in Florida or establish a law office in Florida. An attorney licensed to practice law in a state other than Florida may establish an interstate practice in Florida only if the attorney follows the guidelines of The Florida Bar v. Savitt, 363 So. 2d 559 (Fla. 1978).
An attorney admitted to the practice of law in a state other than Florida may not appear in a Florida court as the representative of a party unless the attorney first seeks permission to appear pro hac vice [for a particular occasion] pursuant to Rule 2.510 of the Florida Rules of Judicial Administration. (It should be noted that this rule does not allow a resident of Florida to appear pro hac vice.) Rule 4-5.5 of the Rules Regulating the Florida Bar describes the legal services an out-of-state attorney can provide in Florida on a temporary basis.
The Summery does not mention NBA or HOA practice. As this is not a court appearance, and as according to the Question a non-lawyer may appear as a QR, it woulds seem that such an appearance does not constitute the practice of law, and thus an out-of-state lawyer would not be committing UPL by representing someone in a NBA proceeding.
It does not appear that charging a fee is an essential element of UPL in Florida (although it is in some states). Thus if Fred may represent Ma\ty as a QR pro bono he may still do so for a fee.