Walks for chaps with a little man at the rear (10)

'walks' is the definition.
(promenading is a kind of walking)

'chaps with a little man at the rear' is the wordplay.
'chaps' becomes 'men' (chap means a man).
'with' is a charade indicator (letters next to each other).
'little man' becomes 'Des' (short for Desmond).
'at' is a charade indicator (letters next to each other) (I've seen this in other clues).
'the rear' becomes 'pro' (I am not sure about this - if you are sure you should believe this answer much more).
'a'+'des'='ades'
'men' next to 'ades' is 'menades'.
'menades' after 'pro' is 'PROMENADES'.

'for' acts as a link.