Came to a big hill, extremely exhausted (8)

'came' is the definition.
(as in coming to or amounting to a certain amount)

'a big hill extremely exhausted' is the wordplay.
'big hill' becomes 'mount' (a mount is a mountain or hill).
'extremely' means to remove the middle letters (only the extremes of the word are used).
'exhausted' with its centre taken out is 'ed'.
'a'+'mount'+'ed'='AMOUNTED'

'to' acts as a link.