link up is a verb meaning "be or become joined or united or linked". It carries 3 recorded senses.
connect, fasten, or put together two or more pieces
“Can you connect the two loudspeakers?”
“Tie the ropes together”
“Link arms”
Definitions, synonyms and semantic relations for link up come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.