Knowledge Graph (KG) completion has been widely studied to tackle the incompleteness issue (i.e., missing facts) in modern KGs. A fact in a KG is represented as a triplet (h,r,t) linking two entities h and t via a relation r. Existing work mostly consider link prediction to solve this problem, i.e., given two elements of a triplet predicting the missing one, such as (h,r,?). This task has, however, a strong assumption on the two given elements in a triplet, which have to be correlated, resulting otherwise in meaningless predictions, such as (Marie Curie, headquarters location, ?). In addition, the KG completion problem has also been formulated as a relation prediction task, i.e., when predicting relations r for a given entity h. Without predicting t, this task is however a step away from the ultimate goal of KG completion. Against this background, this paper studies an instance completion task suggesting r-t pairs for a given h, i.e., (h,?,?). We propose an end-to-end solution called RETA (as it suggests the Relation and Tail for a given head entity) consisting of two components: a RETA-Filter and RETA-Grader. More precisely, our RETA-Filter first generates candidate r-t pairs for a given h by extracting and leveraging the schema of a KG; our RETA-Grader then evaluates and ranks the candidate r-t pairs considering the plausibility of both the candidate triplet and its corresponding schema using a newly-designed KG embedding model. We evaluate our methods against a sizable collection of state-of-the-art techniques on three real- world KG datasets. Results show that our RETA-Filter generates of high-quality candidate r-t pairs, outperforming the best baseline techniques while reducing by 10.61%-84.75% the candidate size under the same candidate quality guarantees. Moreover, our RETA-Grader also significantly outperforms state-of-the-art link prediction techniques on the instance completion task by 16.25%-65.92% across different datasets.