The newly introduced ultra-reliable low latency communication service class in 5G New Radio depends on innovative low latency radio resource management solutions that can guarantee high reliability. Grant-free random access, where channel resources are accessed without undergoing assignment through a handshake process, is proposed in 5G New Radio as an important latency reducing solution. However, this comes at an increased likelihood of collisions resulting from uncontrolled channel access, when the same resources are preallocated to a group of users. Novel reliability enhancement techniques are therefore needed. This article provides an overview of grant-free random access in 5G New Radio focusing on the ultra-reliable low latency communication service class, and presents two reliability-enhancing solutions. The first proposes retransmissions over shared resources, whereas the second proposal incorporates grant-free transmission with non-orthogonal multiple access with overlapping transmissions being resolved through the use of advanced receivers. Both proposed solutions result in significant performance gains, in terms of reliability as well as resource efficiency. For example, the proposed non-orthogonal multiple access scheme can support a normalized load of more than 1.5 users/slot at packet loss rates of ~10^{-5} - a significant improvement over the maximum supported load with conventional grant-free schemes like slotted-ALOHA.