This is the 5783rd most frequent Japanese word.
につれて
"につれて" means "as (something) progresses or changes, something else happens correspondingly."
につれて is used to describe a proportional change: as time progresses, the vividness of memories also increases.
時間が経つにつれて、思い出が鮮やかになっていきます。
As time passes, the memories become more vivid.
につれて expresses correlation: as experience is gained, improvement in skills is observed.
経験を積むにつれて、技術が上達します。
As one gains experience, their skills improve.
につれて indicates a parallel relationship: increase in the number of participants leads to a livelier event atmosphere.