run in
verb
Definitions
(chiefly in the passive) To arrest.
Example: The guys who robbed the bank last week have finally been run in.
To use new machinery at less than full speed, preventing damage.
Example: I have to drive slowly for the first 1,000 miles to run the engine in.
To start a new regime slowly.
Synonyms:phase inTo score (a try).
noun
Definitions
An encounter; a scrape or brush, especially one involving trouble or difficulty.
The end-phase of a competition.
Example: Yahoo Sport's Leicester City blogger Helen Nutter gets ready for the Premier League run-in knowing her side - incredibly - still have a great chance of being crowned champions