Rodent up to taking old root (4)
I believe the answer is:
taro
'root' is the definition.
(taro is a kind of root)
'rodent up to taking old' is the wordplay.
'rodent' becomes 'rat' (rat is a kind of rodent).
'up' is a reversal indicator (in down clue: letters go upwards).
'to taking' is a charade indicator (letters next to each other).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'rat' back-to-front is 'tar'.
'tar'+'o'='TARO'
(Other definitions for taro that I've seen before include "Tropical plant with edible tuberous roots" , "Starchy plant" , "Fortune-telling cards" , "Chinese eddo" , "Shortly pack" .)