、。
Because the train arrived late, they had to change their plans.
Literal
Train [subject-が] late-ly arrive [so-ので], they [topic-は] plans [object-を] change had-to.
遅れて here is the て-form of 遅れる functioning adverbially — 'arriving in a late manner' = 'arrived late.' Chained with the past-tense 到着した outside (not within the single verb) would be awkward; here the entire subordinate clause takes past tense via ~たので. 変更する ('to change, alter') is a formal verb for deliberate modification.