TOKYO, Jan 6 (Reuters) - Japan"s services sector activity expanded at a slower pace in December as growth in new and outstanding business softened and expectations for the 12 months ahead eased to a four-month low. The world"s third-largest economy is expected to rebound in the final quarter of last year after COVID-19 cases fell, as it seeks to catch up with other advanced nations in its recovery from the pandemic"s hit. The final au Jibun Bank Japan Services Purchasing Managers" Index (PMI) dropped to a seasonally adjusted 52.1 from the prior month"s 53.0, which was the highest reading since August 2019. The figure compared to a 51.1 flash reading. "Japanese service sector businesses signalled a sustained expansion in business conditions at the end of 2021," said Usamah Bhatti, economist at IHS Markit, which compiles the survey. "The easing of COVID-19 restrictions allowed customer-facing businesses to operate more freely throughout the final quarter of the year." Firms, however, reported raw material and labour shortages, with employment levels dipping to a 15-month low, while business optimism for the year ahead improved at its weakest pace since September. The private sector as a whole saw cost burdens increase at the year-end amid sustained material shortages and supply chain delays, said Bhatti. "Concerns that disruption would extend into the new year were elevated," he added. The composite PMI, which is calculated using both manufacturing and services, dropped to 52.5 from November"s final of 53.3.