take along, lead, join, connect, party, gang, clique
連 centers on linking things together in a sequence or group: joining, connecting, or leading along. The senses of party, gang, or clique are natural extensions of a connected group of people.
contacting; (making) contact; getting in touch; communication; correspondence; call; message
relation; connection; relevance
continuation; succession; series; sequence
in the company of; accompanied by ...; as a group comprising ...
companion; company
company; lot; people; bunch; gang; pack; guys; group; folks
serialization; serialisation; serial story
union; combination; alliance; confederation; coalition
federation (of states); confederation; commonwealth; union
cooperation; coordination; collaboration; alignment
United Nations; UN
Soviet Union; USSR
consecutive holidays
operating together; working together; being linked (to); being tied (to); being connected (with); interlocking
series; chain; sequence
occurring in succession; doing in succession; series (of incidents); spate
connection; linking; joining; coupling; attaching; junction; concatenation; consolidation (e.g. of company accounts)
league; federation; union
consecutive victories; series of victories; winning streak
regular customer; regular patron; regular visitor; frequenter
association (of ideas); being reminded (of something); suggestion
chain; series; connection
day after day; every day
repeated blows; striking repeatedly; barrage
連 combines 辶 (movement) with 車 (vehicle), suggesting a line of vehicles moving together, which extends to joining or connecting in sequence.
The movement radical 辶 wraps around a vehicle 車. Picture a convoy of cars moving in a line, each one connected to the next, like a gang or party traveling together.
For レン, imagine a long line of rental cars connected in a convoy: rental -> レン, and they all move together like a linked group.