The ESV takes him
to refer to Othniel; thus, Achsah urged Othniel to ask her father for a field. This interpretation follows traditional scholarly consensus. But it has its difficulties.
In the original the referent of the object
him
is ambiguous; it could just as well apply to Caleb as to Othniel, in which case Achsah approaches her father herself, which seems to be confirmed by the following sentences.1In the Hebrew, Othniel
drops out of the story after Judges 1:13. The remainder of Judges 1:14–15, involving only Achsah and her father, describe how this transpired.
2
Thus it seems more likely that Achsah urges her father. What follows in the sentence can be translated as by asking her father for a field.
14 When she came to him, she urged him to ask her father for a field. And she dismounted from her donkey, and Caleb said to her, “What do you want?”