Quickly grabs, coming back, a cat nap in it (5,2)

'quickly grabs' is the definition.
'snaps up' can be an answer for 'grabs' ('snap up' can be a synonym of 'grab'). I'm not certain of the 'quickly' bit.

'back a cat nap in it' is the wordplay.
'back' says the letters should be written in reverse.
'a cat' becomes 'puss' (puss is a kind of cat).
'in it' means one lot of letters goes inside another.
'puss' in reverse letter order is 'ssup'.
'ssup' placed around 'nap' is 'SNAPS UP'.

'coming' is the link.

Can you help me to learn more?