Answer
The exact definition of a "new ship" changes depending on the specific convention or annex being referenced, as it establishes the precise date from which a set of technical rules becomes mandatory.
As per MARPOL Annex VI (Regulation 2.2.18 - Energy Efficiency / EEDI):
"New Ship" means a ship for which the building contract is placed on or after 1 January 2013; or in the absence of a building contract, the keel of which is laid on or after 1 July 2013; or the delivery of which is on or after 1 July 2015.
As per SOLAS Chapter II-1 (Construction - Structure, Stability, Installations):
Unless expressly provided otherwise, "new ship" means a ship the keel of which is laid or which is at a similar stage of construction on or after 1 January 2009.
as per SOLAS Chapter I, Regulation 2(k), a new ship means a ship whose keel is laid or which is at a similar stage of construction on or after 25 May 1980. A similar stage of construction means construction identifiable with a specific ship has begun and assembly has commenced comprising at least 50 tonnes or 1% of the estimated mass of all structural material, whichever is less. However, the definition is convention-specific, and later SOLAS chapters or amendments may prescribe different application dates.