Jǐngēnzhe dìyī shēng léi xiǎng, dàyǔ jiù xià le qǐlái.
Right after the first clap of thunder, heavy rain started falling.
Tips
grammar
紧跟着 is 紧跟 (to follow closely) + 着 (aspect particle indicating continuation). It can function as an adverb meaning 'immediately after' or as a verb phrase meaning 'following closely behind'.