The most common and most likely answer to this crossword clue is the 3 letter word WAN
I've seen this crossword clue in The Times
W
A
N
Buddy explains!

The straight part
We know that "Pale and sickly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pale and sickly = wan.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 WAN mean?
WAN noun- The quality of being wan; wanness.
- Pale, sickly-looking.
- Dim, faint.
- Bland, uninterested.
- The digit or figure 1.
- The neutral element with respect to multiplication in a ring.
- A one-dollar bill.
- One run scored by hitting the ball and running between the wickets; a single.
- A joke or amusing anecdote.
- A particularly special or compatible person or thing.
- (leet) Used instead of ! to amplify an exclamation, parodying unskilled typists who forget to press the shift key while typing exclamation points, thus typing "1".
- A girl or woman.
- To conquer, defeat.
- To reach some destination or object, despite difficulty or toil (now usually intransitive, with preposition or locative adverb).
- To triumph or achieve victory in (a game, a war, etc.).
- To gain (a prize) by succeeding in competition or contest.
- To obtain (someone) by wooing; to make an ally or friend of (frequently with over).
- To achieve victory.
- To have power, coercion or control.
- To obtain (something desired).
- To cause a victory for someone.
- To extract (ore, coal, etc.).
- To dry by exposure to the wind.