The most common and most likely answer to this crossword clue is the 7 letter word ROSEATE
I've seen this crossword clue in The Times
R
O
S
E
A
T
E
More clues leading to the result ROSEATE
Buddy explains!

The straight part
We know that "reddish" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case reddish = roseate.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.
What does ROSEATE mean?
ROSEATE adjective- Like the rose flower; pink; rosy.
- Full of roses.