One used for skipping or doing somersault at gym (4)
I believe the answer is:
rope
'one used for skipping' is the definition.
(skipping rope)
'or doing somersault at gym' is the wordplay.
'doing somersault' says the letters should be written in reverse (in a down clue, letters flip up).
'at' says to put letters next to each other.
'gym' becomes 'pe' (short for Physical Education).
'or' in reverse letter order is 'ro'.
'ro'+'pe'='ROPE'
(Other definitions for rope that I've seen before include "Lasso?" , "Enough to hang one?" , "Stranded fastener" , "A thick strong cord" , "Noose" .)