Compiling from source requires two libraries: libdeflate and libisal. In addition, cmake is required as well.
Source code is here
libisal requires nasm to compile here
1. In the source folder run

configure --prefix=/home/.hub_local
make
make install

2. download and build libisal

git clone https://github.com/intel/isa-l.git
mkdir /home/.hub_local/lib64
cd isa-l
./autogen.sh
./configure --prefix=/home/.hub_local --libdir=/home/.hub_local/lib64
make
sudo make install

3. download and build libdeflate

git clone https://github.com/ebiggers/libdeflate.git
cd libdeflate
cmake -B build
cmake --build build
cmake --install-prefix=/home/.hub_local build
cmake --install build

4. download and build fast

git clone https://github.com/OpenGene/fastp.git

Need to edt the Make file in the fastp folder and set the following lines:

PREFIX ?= /home/.hub_local
BINDIR ?= $(PREFIX)/bin
INCLUDE_DIRS ?=  /home/.hub_local/include
LIBRARY_DIRS ?= /home/.hub_local/lib64 /home/.hub_local/lib

Then compile

# build
cd fastp
make
# Install
make install

To run the binary you need to set the library path

export LD_LIBRARY_PATH=/home/.hub_local/lib64

That should do it.