Rhino runs into deep (5)
I believe the answer is:
brass
'rhino' is the definition.
(I've seen this before)
'runs into deep' is the wordplay.
'runs' becomes 'r' (cricket abbreviation).
'into' indicates putting letters inside.
'deep' becomes 'bass' ('bass' can be a synonym of 'deep').
'r' put inside 'bass' is 'BRASS'.
(Other definitions for brass that I've seen before include "some musicians!" , "Alloy (associated with muck)" , "Gall" , "Money - cheek!" , "Instruments, alloy" .)