Usage Note
Resserrer means to tighten something that has loosened (resserrer une vis) or, figuratively, to reinforce ties: resserrer les liens (to strengthen bonds). The reflexive se resserrer is very common: les rangs se resserrent (the ranks are closing) or l'étau se resserre (the noose is tightening). It is distinct from serrer (to grip/tighten once) by implying a re-tightening.
Examples
"Il faut resserrer les liens entre nous."
Natural Translation
We need to strengthen the bonds between us.

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