A clause is the smallest unit of English grammar and it is made up of a subject and a verb. To have clauses, we need phrases and with the combination of two or more clauses we get sentences. Grammar Bank
in the same page there is an example:
A famous celebrity had an unfortunate accident a long time ago (first clause) when he didn't use his safety equipment (second clause) and injured his left arm severely. (third clause)
Where is the subject in the third clause?