To Understand, To Be Aware Of, To Consent, To Agree
Transitive verb and Ichidan verb
こころえる
このお方をどなたと心得るか。
Does anyone know who this woman is?
Remember how you learned that 心得 means "knowledge"? Well the verb version of that is to know. (You know it deep in your heart.)
The readings for this word are both kun'yomi readings. You learned them when you learned the kanji, so you should be able to read this on your own.