Downing Street leader's about to pursue German girl (9)
I believe the answer is:
ingestion
'downing' is the definition.
(as in downing food or drink)
'street leader's about to pursue german girl' is the wordplay.
'street' becomes 'st' (abbreviation).
'leader's about' becomes 'ion' (I can't justify this - if you can you should give a lot more credence to this answer).
'to pursue' means one lot of letters go next to another.
'german girl' becomes 'Inge' (German girl's name).
'st'+'ion'='stion'
'stion' put after 'inge' is 'INGESTION'.
(Another definition for ingestion that I've seen is " Taking in".)