There are two official tests of Chinese (Mandarin), one in mainland China and one in Taiwan:
Hanyu Shuiping Kaoshi (汉语水平考试), translated as Chinese Proficiency Test is the ONLY official test of Mandarin in mainland China for non-native speakers. It is under the responsibility of Hanban, China National Office for Teaching Chinese as a Foreign Language ((中国国家对外汉语教学领导小组办公室). For more information, please consult https://www.hsk.org.cn/english/default.aspx.
Test of Chinese as a Foreign Language (TOCFL), formerly known as the Test Of Proficiency-Huayu or TOP is the test used in Taiwan for Mandarin as a foreign language. It is administered by the Steering Committee for the Test Of Proficiency-Huayu ( 國家華語測驗推動工作委員會), under the direction of the Ministry of Education. For more information, please consult https://www.tw.org/tocfl/.
For postgraduate admissions, you are most likely to be asked for TOCFL level 4 (out of 7) upwards and a HSK 6 (out of 11) upwards.
To compare the levels in these two tests, visit the following link: