A flapper seat assembly that is replaceable with respect to a safety valve positioned downhole in a wellbore is described herein. For example, the safety valve can be positioned downhole in a wellbore and can include a housing. Additionally, the safety valve can include a flow tube that can be coupled to a downhole tool. The flow tube can be removed from the safety valve in response to a first force applied to the flow tube. A portion of the flapper seat assembly can be detached from a housing profile to remove the flapper seat assembly from the wellbore in response to a second force applied to the flapper seat assembly. After removing the flapper seat assembly, a second flapper seat assembly can be attached to the safety valve.