The most common and most likely answer to this crossword clue is the 8 plus 10 letter word STALLING (SUCKLING)
I've seen this crossword clue in The Guardian
S
T
A
L
L
I
N
G
(
S
U
C
K
L
I
N
G
)
Buddy explains!
The straight part
We know that "playing for time" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case playing for time = stalling (suckling).The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.