Final answer:
After the extraction of a first primary molar, monitoring the dental arch development is crucial for ensuring proper permanent teeth alignment, which may also necessitate a space maintainer.
Step-by-step explanation:
The most appropriate treatment following the extraction of a first primary molar in a 4-year-old child is regular assessment of arch development. This is because it is important to monitor the growth and development of the child's dental arch to ensure proper spacing and alignment for the eventual eruption of permanent teeth.
Inserting a space maintainer may also be considered, depending on the individual case, to prevent space loss due to the premature extraction of a primary tooth, which can affect the alignment of future permanent teeth.