The most common and most likely answer to this crossword clue is the 5 letter word LIMPS
L
I
M
P
S
More clues leading to the result LIMPS
Buddy explains!

The straight part
We know that "Moves unsteadily" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case moves unsteadily = limps.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 LIMPS mean?
LIMPS noun- An irregular, jerky or awkward gait.
- A scraper for removing poor ore or refuse from the sieve.
- To walk lamely, as if favouring one leg.
- (of a vehicle) To travel with a malfunctioning system of propulsion.
- To move or proceed irregularly.
- To call, particularly in an unraised pot pre-flop.
- A scraper of board or sheet-iron shaped like half the head of a small cask, used for scraping the ore off the sieve in the operation of hand-jigging.
- To be inadequate or unsatisfactory.
- To happen; befall; chance.
- To come upon; meet.