"Making trial of everything, with trust in new joy, and stirring the human kindness in all eyes that looked on her."
If it is an independent clause, could you please tell which is the subject and which is the verb.
"Making trial of everything, with trust in new joy, and stirring the human kindness in all eyes that looked on her."
If it is an independent clause, could you please tell which is the subject and which is the verb.
That is not a grammatical /sentence/ at all, by itself!
Here is the full sentence, which /is/ grammatical:
Eppie was a creature of endless claims and ever-growing desires, seeking and loving sunshine, and living sounds, and living movements; making trial of everything, with trust in new joy, and stirring the human kindness in all eyes that looked on her.
Since the part you quote above cannot stand on its own and have meaning, it is a subordinate clause. Eppie is the subject, even though she does not appear in the clause itself. The "making..." here is a present participle phrase, which functions somewhat like an adjective. Because the "to be" verb was used in the first part of the clause, the mood of that verb carries over to the verb "making" and this is an indicative statement about Eppie.
This is a complex sentence! Perhaps think of the clausal structure as a shorthand for writing each of the sentences starting "Eppie was..." simultaneously:
Eppie was a creature of endless claims...
Eppie was seeking and loving sunshine...
Eppie was making trial of everything...
and so forth. It's not quite exactly the same as if Eliot had done that, but it's the general idea.