RIP! Old females depart quickly (4,3)
I believe the answer is:
tear off
'depart quickly' is the definition.
(to tear off is to run away)
'rip old females' is the wordplay.
'rip' becomes 'tear' (synonyms).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'females' becomes 'ff' (the abbreviation for female repeated).
'tear'+'o'+'ff'='TEAR OFF'
(Other definitions for tear off that I've seen before include "Depart hurriedly" , "Forcibly remove" .)