In D&D 5th edition's Forgotten Realms setting what ability is required for a creature to be able to grant a creature warlock powers?
There are not currently any hard and fast rules for what makes a viable warlock patron. What we do know is that the following all qualify:
immensely powerful fey (Titania, Oberron, Hyrsam, the Queen of Air and Darkness, the Prince of Frost)
immensely powerful demons and devils (Baazka, Belaphoss, Eltab, Errtu, Gargauth, Lorcan, Malkzid, Wendonai)
immensely powerful old ones (Dendar the Night Serpant, Ghaunadaur, Kezef, Moander, Tyranthraxus, Zargon)
immensely powerful undead (no list available)
All of this information comes from the Sword Coast Adventurer's Guide.
One of the important things to note is the 'immensely powerful' part of the description - these are all quasi-deities according to the Divine Rank scale in the DMG, and most if not all would be considered vestiges.