High temperature air source heat pumps (HT-ASHPs) have a good potential for retrofitting the domestic built environment in the UK because they can directly replace existing fossil-fuelled boilers without the requirement of modification of the heat distribution systems, which makes them cost-competitive regarding retrofit aspect and allows the UK to attain the carbon cut target. However, a widespread of these heat pumps would pose a challenge to the grid demand. In this study, a demand-side management (DSM) strategy was developed to address this issue. Thermal energy storage (TES) was integrated with HT-ASHPs to perform the developed DSM, which aimed at levelling off the grid demand by means of switching on the heat pump to charge the TES where there was low demand (midnight to 7am) and switching off the heat pump during peak hours (4pm to 7pm). The reference case was a mid-terraced dwelling equipped with traditional wet radiators, which is a typical house in Northern Ireland. TRNSYS simulations were used to run the developed DSM. Different TES sizes and set point temperatures were examined to seek the optimum values. The study also analysed with different electricity tariffs including flat rate, Economy 7 (the electricity is cheaper in night time than daytime) and Powershift (the electricity is divided into three bands: low, normal and peak). Results showed that both the tank size and setpoint temperature strongly affected the heat pump performances. The TES size of 1m³ and set point of 75˚C were the ideal parameters because it could shift wholly the 3-hour peak demand. The effects of the developed DSM on the grid and how the tariffs affected the system have also been discussed in this paper.