Once there, he would cling to the hand-rail... (Para. 4)
Meaning: Once (= As soon as) he got there, he would hold on to the hand-rail for support.
"Once" as a conjunction introduces an adverbial clause in which the subject and the verb "be" can often be omitted. Look at the following example:
Once (they are) in bed, the children usually go to sleep very quickly. 一上床, 这些孩子通常很快就睡着了。
cling to: hold tightly; refuse to let go
They clung to one another for support. 他们互相紧抓住对方, 以相互支撑。
She still clings to the idea that her son is alive. 她仍抱着一个信念: 儿子还活着。