Gone Trapping
Answer: ENSNARE
Eric Wei

This puzzle has both crossword clues and cryptic clues. Crossword clues are ordered alphabetically by clue, while cryptic clues are ordered alphabetically by answer. Their answers are as follows (a detailed explanation of the cryptic clues can be found at the end of the solution):

Traps (crossword-style clues):

Animals (cryptic clues):

After solving some of the clues, solvers may realize that some of the crossword clue answers and cryptic clue letters share many letters in common. This provides a pairing between every crossword clue answer and cryptic clue answer. Also, because every crossword clue is associated with a number between 1 and 6, it makes sense to index into the cryptic clue answers:

Animal Trap Extras Index Letter
LINENS LIES NN 6 S
MENTAL METAL N 6 L
PAINED PAID NE 3 I
PLANET PLANT E 4 N
RENOWN RENO WN 4 O
RUSSET RUST SE 1 R
SEEING SING EE 1 S
SEXIST EXIT SS 2 E
SHREWD SHRED W 4 E
SPARSE PARSE S 3 A
SWEDEN EDEN SW 6 N
WIDOWS I DOS WW 6 S
The extra letters are all either N, E, S, or W (the four cardinal directions). Furthermore, they are all unique and 1-2 letters long. This (along with the flavortext) suggests we should map out these locations.
LINENS
S
RENOWN
O
MENTAL
L
PAINED
I
WIDOWS
S
SHREWD
E
WAGON PLANET
N
SEEING
S
SWEDEN
N
SPARSE
A
RUSSET
R
SEXIST
E
The letters, in order, spell SOL (solution) IS ENSNARE.
A more detailed explanation for the cryptic clues: