Edge back deep with player on field and cover for prop (6,4)

'cover for prop' is the definition.
'pillow slip' can be an answer for 'cover' (thesaurus). I'm not certain of the 'for prop' bit.

'edge back deep with player on field' is the wordplay.
'edge' becomes 'lip' (lip is a kind of edge).
'back' says the letters should be written in reverse.
'deep' becomes 'low' (similar in meaning).
'with player on field' becomes 'slip' (I am not sure about this - if you are sure you should believe this answer much more).
'lip' backwards is 'pil'.
'pil'+'low'+'slip'='PILLOW SLIP'

'and' is the link.

Can you help me to learn more?