Ride moving up South Beach (5)
I believe the answer is:
shore
'beach' is the definition.
(I've seen this before)
'ride moving up south' is the wordplay.
I cannot quite see how this works, but
'south' could be 's' (synonyms) and 's' is found in the answer.
The remaining letters 'hore' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
(Other definitions for shore that I've seen before include "Horse (anag.)" , "support being only temporary?" , "coastal area" , "Beam" , "Beach; prop (up)" .)