Software testing relates to the process of accessing the functionality of a program. To ensure conformance, test engineers often generate a set of test cases to validate against the user requirements. When dealing with large line of codes (LOCs), there are potentially issues of redundancy as new test cases may be added and old test cases may be deleted during the whole testing process. To address redundancy issues, many useful strategies (e.g. HGS, GE, and GRE) have been developed in the literature. These strategies often put focus on getting the most minimum test suite size but give poor emphasis on test prioritization (i.e. ordering of tests). Here, as most testing activities happen toward the end of software development, testers are often forced to consider partial test suite, that is, to be in line with the project deadline. In this manner, some impactful defects may be missed owing to the need to accommodate deadline shift from earlier development activities. In order to address these issues, this paper highlights our on-going work on the development of a novel test redundancy reduction strategy based Late Acceptance Hill Climbing, called (LAHCS).  LAHCS is the first known strategy that adopts Late Acceptance Hill Climbing Algorithm for test redundancy reduction and prioritization.