He was never technically the director of SHIELD. SHIELD was defunct when he took over the "top cop" position and, rather than restarting it, Cap decided to just expand the Avengers and have them deal with everything.
SHIELD later got restarted independently from Dum Dum and Gabriel Jones' Howling Commandos PMC and the remnants of Fury's Caterpillar program with Daisy Johnson as its new director. Although she hasn't really done much since. I think Cap still outranks her too, since he basically drafted her into the Avengers recently.
And now Marcus Johnson is set to replace Nick Fury himself because he's black and the movies exist. Not sure whether he'll take over SHIELD as well, but it would probably be a fairly safe bet.