Completion date is mentioned in this document from 1925 http://www.legco.gov.hk/1925/h250514.pdf (thanks to Annelise for the link):
St. Peter's Church was erected in 1871 on a portion of the present site of the Sailors' Home. The cost of the building was defrayed by subscriptions raised in the Colony and elsewhere and by
Although that suggests the church was built for the use of the sailors, the history of the Sailor's Home (https://themarinersclubhk.org/our-history--.html) says the church started out for use by the local community, then only later was it used by sailors:
1863: A Sailors' Home was founded in Hong Kong when a hostel building was provided at West Point by a number of local firms. The firm of Jardine Matheson took a prominent part in this St. Peter's Church was built in the compound & initially was used by locally resident Europeans and was later to become the Seamen's Church.
1884: The work of The Missions to Seamen began in Hong Kong and in 1885 permission was given for the Chaplain to use St. Peter's Church in the Sailors' Home compound.
The 1925 document above said the church was going to move:
The site of the Church is now required for public purposes and the authorities of the Church would prefer to have a quieter neighbourhood than the present one. The Government accordingly propose to grant a new site for the Church and to contribute the sum of $50,000 for the erection of a new Church.
However I'm not sure how long the church remained at this site before it was demolished.