Crossed a hill crest in the outskirts of Brentwood (7)

'crossed' is the definition.
(bridging is a kind of crossing)

'a hill crest in the outskirts of brentwood' is the wordplay.
'a hill crest' becomes 'ridge' (I've seen this in another clue).
'in the' indicates putting letters inside.
'outskirts of' means to remove the middle letters (only letters on the outskirts).
'brentwood' with its centre taken out is 'bd'.
'ridge' inserted into 'bd' is 'BRIDGED'.