Former park with a turn on, including gym, etc. (5)

'former park' is the definition.
I know nothing about this answer so I cannot judge whether it can be defined by this definition.

'a turn on including gym etc' is the wordplay.
I cannot quite see how this works, but
'turn' could be 'u' (a 'U-turn' is a kind of turn) and 'u' is found within the answer.
'on' is found in the answer.
'gym' could be 'pt' and 'pt' is present in the answer.
No letters remain.
This explanation may well be incorrect...

'with' is the link.

Can you help me to learn more?