Brockman started as a cadet of Straits Settlement Service in December 1886 and was appointed as private secretary to the John Frederick Dickson in October 1887. In June 1889, he was appointed to be the Registrar of Deeds for the Settlement of Penang and on 1 June 1890 was appointed the Third Magistrate of Penang and continue as Acting Collector of Land Revenue, Penang. In July 1891, he was appointed as District Officer of Bukit Mertajam and Coroner of Province Wellesley and in February 1892 was the acting 2nd Assistant Colonial Secretary to relieve Mr A H Capper who went on home sick leave. On 22 March 1892, he was appointed as the District Officer of Penang and in November 1895 and June 1896, he was again appointed as acting 2nd Assistant Colonial Secretary. In June 1896, he was appointed as Collector of Land Revenue, Singapore and in August 1897, Assistant Colonial Secretary and Clerk of Councils. On 24 August 1898, he was the Collector of Land Revenue, Malacca and in 1899 was the acting First Magistrate in Singapore. In February 1902, he was appointed the Senior District Officer of Province Wellesley and in September 1902 commissioner of the Courts of Requests in Singapore while continuing to act as first magistrate in Singapore. In September 1903, he was appointed as Assistant Colonial Secretary. and was the Acting Colonial Secretary of Straits Settlements between April 1905 and July 1906 when Mr F G Penney was on a furlough. In April 1907, he was appointed Acting Federal Secretary and confirmed the appointment in July 1907. On 15 April 1908, he was the acting Resident of Perak and in November 1908 was appointed as the Resident of Pahang. On 1 February 1911, he was appointed Colonial Secretary of Straits Settlements and on 4 September the same year, he arrived at Kuala Lumpur to take up the appointment of Chief Secretary, FMS. From 1921 to 1925, Brockman was an agent of the Malay States Information Agency in London, succeeding Sir W T Taylor who has retired from the position.
Personal life
Brockman married widow Mrs F. S. B. Gaffney on 28 October 1907. He retired in 1920, after 34 years of civil service in Malaya and Straits Settlements. He continue to be active after retirement and was an agent of Malay States Information Agency, based in London.