To Know
To Understand, To Be Aware Of, To Consent, To Agree
transitive verb, ichidan verb
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.)
こころえる
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.
このお方をどなたと心得るか。
Does anyone know who this woman is?