British Library - India Office Records
IOR/Z/O/6/2 - Index to Personnell Records (H-Z, 1794-1841). It is possible that he left prior to 1794 due to the re-organisation
IOR/Z/0/1/1 - Bonds of Overseas Staff of the EIC (1700-1800). This primarily records bonds relating to senior appointment which may explain the absence of any records
IOR/F/1/1 - Court Directors Minutes (1784-1793) - only senior appointments noted
IOR/F/1/2 - Court Directors Minutes (1794-1804) - only senior appointments noted
IOR/O/5/24 - Establishment Details (1766-1800) - only senior appointments noted
IOR/O/5/25 - Establishment Summaries (1766-1800) - only senior appointments noted
I have checked the shipping journal of the Egmont (IOR/L/MAR/B/535E) and Francis (IOR/L/MAR/B/443) and no O'Hara's are mentioned, but unless they died or were responsible for some incident they would have not have been.
The National Archives (Public Record Office) * indicates information found
Admiralty: Naval Hospitals' and Hospital Ships' Musters, and Miscellaneous Journals - Mauritius
(1823-1828) ADM102/575
Records of the Prerogative Court of Canterbury
PROB31/1020 - Will of Lt Andrew Best d. 1807 also in 33rd Regiment of Foot
Commander-in-Chief: Loose in-letters: Dispatches from Calcutta (1808-1811),
on the Vellore massacre (1805), from Mauritius (1812)
(1805-1857) WO1/360
War Office and predecessors: Indexes to Out-letters
Administrative. Indexed under Regts
(1792-1796) WO2/1
(1798) WO2/2
Regimental
(1791-1796) WO2/36
(1796-1803) WO2/37
(1803) WO2/38
War Office: Secretary-at-War, Out-letters
General Letters
(01.1796 - 03.1796) WO4/163
(03.1796 - 05.1796) WO4/164
(05.1796 - 09.1796) WO4/165
East Indies (1792-1796)
(1795) WO4/298
(1796) WO4/299
(1805-1810) WO4/514
(1810-1813) WO4/515
(1813-1815) WO4/516
(1815-1816) WO4/517
(1817-1820) WO4/518
(1820-1836) WO4/519
Establishments: Regimental (1819-1829)
WO4/720
Private (series 1) (1782-1798)
WO4/983
Commissary General of Musters Office and successors: General Muster Books and Pay Lists
33rd Foot 1st Battalion (1791-1812)
* (1791-1804) WO12/4804
* (1808-1809) WO12/4805
* (1810) WO12/4806
* (1811) WO12/4807
* (1812) WO12/4808
52nd Foot 1st Battalion (1780-1799)
* (1780 - 1797) WO12/6241
* (1798 - 1799) WO12/6242
56th Foot 1st Battalion (1811-)
* (1811) WO12/6556
* (1812) WO12/6557
* (1813) WO12/6558
* (1814) WO12/6559
* (1815) WO12/6560
* (1816-1817) WO12/6561
* (1818-1819) WO12/6562
* (1820) WO12/6563
56th Foot 2nd Battalion (1811-)
* (1811) WO12/6625
* (1812) WO12/6626
* (1813) WO12/6627
(1814) WO12/6628
* (1815) WO12/6629
* (1816-1817) WO12/6630
War Office: Secretary-at-War, Registers
Notification books to the Secretary of State
(1795) WO25/160
(1795) WO25/161
(1796) WO25/162
* (1798) WO25/167 - transfer to 33rd Regiment vice Fennell
(1798) WO25/168
Succession books (series 2) : general
(1796/97) W025/225
* (1797/99) W025/226 - confirms Lawrence as Ensign
Description and Succession Books (Regimental)
(1783-1806) WO25/405
Services or officers on Full and Half Pay (Returns to the circular letter 27 Oct., 1828)
( -1828) WO25/770
( -1828) WO25/771
Reports of Officers' Marriages
(1799-1843) WO25/3239
Office of the Commander-in-Chief
Memoranda and Papers
(05.1796) WO31/46
(05.1796) WO31/47
(06.1796) WO31/48
(07.1796) WO31/49
(08.1796) WO31/50
(09.1796) WO31/51
(10.1796) WO31/52
(11.1796) WO31/53
(12.1796) WO31/54
(01.1797) WO31/55
(04.1797) WO31/58
(11.1797) WO31/65
* (02.1799) WO31/80 - this confirmed the entry in the London Gazetter to be Lt vice Fennell
(09.1806) WO31/213
(12.1806) WO31/219
* (08.1819) WO31/478 - this confirmed his Brevet to Major
(1821) WO31/509 - Sale of Commission (filed under Brough)
Registered Files (General Series)
Certificates of births, baptisms marriages and deaths extracted from old personal papers
(1777-1892) WO32/8905 (L-P)
(1790-1888) WO32/8914 (L-P)
(1814-1872) WO32/8918 (L-P)
War Office: Officers' Birth Certificates, Wills and Personal Papers
(1755-1908) WO42
Officers' commissions
(1780-1874) WO43/1059
Letters to Commissariat Officers stationed abroad: Mauritius and St. Helena
(1810-1817) WO58/110
The Limerick City, Royal Field (Reserve) Artillery, formerly Limerick City (Militia) Digest of Service of the Regiment
(1793-1909) WO68/59
Royal Hospital Chelsea: Soldiers Service Documents: 56th Foot: Mas - Pyn
(1760-1854) WO97/693
War Office: General Sir Robert Brownrigg, Military Secretary to Commander in Chief
Out-Letter Books: to Commander in Chief
(04.1795-08.1798) WO133/1
(08.1798-09.1805) WO133/2
(09.1796-12.1797) WO133/3
Home Office: Military Entry Books
(1796-1797) HO51/10 (Only Militia not relevant)