| Cover | May 10, 2022 |
| Cover [Abstract] | |
| Document Type | 8-K |
| Amendment Flag | false |
| Document Period End Date | May 10, 2022 |
| Entity File Number | 001-41384 |
| Entity Registrant Name | Hanover Bancorp, Inc. /NY |
| Entity Central Index Key | 0001828588 |
| Entity Tax Identification Number | 81-3324480 |
| Entity Incorporation, State or Country Code | NY |
| Entity Address, Address Line One | 80 East Jericho Turnpike |
| Entity Address, City or Town | Mineola |
| Entity Address, State or Province | NY |
| Entity Address, Postal Zip Code | 11501 |
| City Area Code | 516 |
| Local Phone Number | 548-8500 |
| Written Communications | false |
| Soliciting Material | false |
| Pre-commencement Tender Offer | false |
| Pre-commencement Issuer Tender Offer | false |
| Title of 12(b) Security | Common Stock, par value $0.01 |
| Trading Symbol | HNVR |
| Security Exchange Name | NASDAQ |
| Entity Emerging Growth Company | true |
| Elected Not To Use the Extended Transition Period | false |
