Thomas Bird applied for a publican's license for the Stockton Arms in 1842, however the application was refused by the bench.
The first publican's licence in Stockton was issued to Zachariah Shaw Moore who held the license in 1847 and 1848. 
When the Stockton Arms was advertised for sale in November 1848, it was the only public house at Stockton and said to be situated in the midst of a considerable manufacturing population. It catered for the employees of the tweed factory run by Fisher and Donaldson which had opened in 1844.
The premises of the hotel was sold together with the Miners' Arms of Newcastle for £520 in 1849.
The Stockton Arms probably closed its doors after the Tweed Factory was completely destroyed by fire in 1851.
General Washington Hotel
In the 1860s the leading hotel was the General Washington, run by Mr. McFarlane. Dances were held at the General Washington on Saturday and holiday nights, parties being conveyed to and from the Market Wharf at Newcastle free of charge at all hours. 
A correspondent to the Maitland Mercury visited Stockton in 1861. He described the hotel at that time......After spending an hour very pleasantly, we walked towards the ruins of the Cloth Factory (unfortunately burnt down some few years since). On our way we passed several neat and clean looking cottages, with pretty gardens ; part of the factory was occupied, as a butcher's shop, and part used for fishing materials, with some outlay a portion of the premises might be repaired so as to permit of their being used as stores or work-shops. After viewing the out-houses, &c., we retraced our steps and strolled under the shade of the trees towards what is known as the Salt Works. On our way we noticed the Washington Hotel, which has undergone considerable improvement. The present proprietor, Mr. McFarlane, was busily engaged making extensive alterations inside the hotel, while others were busy outside making tea gardens, archery ground, skittle alley, etc.
 Ancestry.com. New South Wales, Australia, Certificates for Publicans' Licences, 1830-1849, 1853-1860
 The Newcastle Sun (NSW : 1918 - 1954) Mon 27 May 1940
 The Maitland Mercury and Hunter River General Advertiser (NSW : 1843 - 1893) Tue 23 Jul 1861