First of all, this question shares the same context with another Q&A asking for the meaning of 手{て}かがり.
What follows is an excerpt from N2新完全マスター, in particular the section 問題紹介 where they are explained the different exercises that appear in the N2 Japanese Language Proficiency Test:
I have trouble understanding the following sentence:
【例題3】では「〜について」「〜に対する」という文法形式を手がかりに、その前後にどんな言葉がくるかを考えます。
Where is the verb corresponding to the highlighted particles を and に? It sure can't be 考えます because it takes another を.
Finishing the relative clause adverbially with 手がかりに feels incomplete and abrupt. I found this related Q&A where they explain that sometimes the verb is omitted in the construction AをBに, but this sentence doesn't seem to fit the typical examples with body parts and such listed in the accepted answer.
Is して implied here, as explained in the alternative answer of the same Q&A, or what is going on?
【例題3】では「〜について」「〜に対する」という文法形式を手がかりに[して]、その前後にどんな言葉がくるかを考えます。In the example 3, [make a hint of] the grammar forms について and に対する, and think of what word comes before and after them.
