Continual learning requires large language models to acquire new knowledge and capabilities while retaining what they have learned. Fine-tuning and replay support acquisition and retention, but deciding whether incoming examples need supervision and which historical examples to revisit remains a challenge. We propose Compatibility-Aware Memory Replay (CAMR), an adaptive framework that jointly controls current-example supervision and historical replay. CAMR combines compatibility checks with a learned memory gate to guide an online policy over three actions: learning incoming examples with general replay, jointly reinforcing compatible related examples, and skipping direct supervision of verified mastered duplicates. The policy learns from acquisition, retention, and training-cost feedback under a bounded per-arrival replay budget. We evaluate CAMR with Qwen3-8B-Base on continual factual updating and cross-task and cross-domain learning. On WikiBigEdit, CAMR consistently leads evaluated methods in Original Match from 3K to 100K facts, reaching 93.66% after just 3K facts and surpassing Full-history Replay (LoRA) after 100K facts. It also achieves the highest final scores on all four selected TRACE tasks and maintains or improves earlier-task performance relative to post-acquisition levels in a sequence spanning financial question answering, mathematical reasoning, code generation, and summarization.

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