Run after small girl, who may be on thin ice (6)
I believe the answer is:
skater
'who may be on thin ice' is the definition.
(as in an ice-skater)
'run after small girl' is the wordplay.
'run' becomes 'r' (cricket abbreviation).
'after' says to put letters next to each other.
'small' becomes 's' (abbreviation - e.g. clothes size).
'girl' becomes 'kate' (girl's name).
's'+'kate'='skate'
'r' after 'skate' is 'SKATER'.
(Other definitions for skater that I've seen before include "Ice sportsman" , "Performer on ice" , "One using blades (or rollers?)" , "Rink glider" , "Winter sports person" .)