Disreputable monarchy loses my support (6)
I believe the answer is:
anchor
'support' is the definition.
(I know that anchor is a type of support)
'disreputable monarchy loses my' is the wordplay.
'disreputable' is an anagram indicator (I've seen this in other clues).
'loses' suggests deleting specific letters.
'monarchy' with 'my' removed is 'onarch'.
'onarch' is an anagram of 'ANCHOR'.
(Other definitions for anchor that I've seen before include "Device to hold a ship in place" , "Weight attached to sea bed" , "Charon (anag.); Styx ferryman" , "I present" , "A weight to secure in place" .)