这句话不是很完整,前面应该还有一些内容.我加上去看下.
They didn't chat.They began to work instead,to make life better 如果instead后面有个逗号,你会更好理解.后面的不定式与它无关,是作目的状语的.
他们不再聊天,相反,他们开始工作,目的是让生活更好些.
instead是个介词,可以放在句首或句末.如：
They didn't chat.Instead they began to work.
也可构成词组：instead of 后跟名词或动名词.
They began to work instead of chatting.