1. The same letters, in the same, consecutive order, will change each word into a new one:

LORE
ROVE
EACH

2. The same letters, in the same, consecutive order, will complete each partial word below:

OT
TH

3. The same letters, in the same, consecutive order, will change each word below into a new one:

ION
IMP
FOR
PRICING

Answers:

1. The letters are IMP:

IMPLORE
IMPROVE
IMPEACH

2. The letters are DEP:

DEPOT
DEPTH

3. The letters are ACT:

ACTION
IMPACT
FACTOR
PRACTICING

Credit #3:
NY Times Crossword
Joe DiPietro
DISAPPEARING ACT