Intersection

Below we set processes with a function in a QTimer.singleShot, to allow multi-execution, but it is not mandatory according your context.

import os
import shutil
 
myPath = r'C:\\Users\\georg\\Downloads\\'
 
project = QgsProject.instance()
project.removeAllMapLayers()
project.clear()
iface.mapCanvas().refresh()
 
peaks = QgsVectorLayer(myPath + 'peaks_selection/peaks_selection.shp', 'Peaks', 'ogr')
iris = QgsVectorLayer(myPath + 'iris/iris.shp', 'IRIS', 'ogr')
 
QgsProject.instance().addMapLayer(peaks)
QgsProject.instance().addMapLayer(iris)
 
# Intersection function
def myIntersection():
    # Directory for created layer
    _peaks_intersection = myPath + '_peaks_intersection'
    if os.path.isdir(_peaks_intersection) == True:
        shutil.rmtree(_peaks_intersection)
    if os.path.isdir(_peaks_intersection) == False:
        os.mkdir(_peaks_intersection)
 
    # Intersect peaks and IRIS
    peaks_intersection_path = _peaks_intersection + r'\\peaks_intersection.shp'
    processing.run('qgis:intersection', { \
    "INPUT": peaks, \
    "OVERLAY": iris, \
    "INPUT_FIELDS": ["OSM_ID", "NAME", "OTHER_TAGS"], \
    "OVERLAY_FIELDS": ["CODE_IRIS", "NOM_COM"], \
    "OVERLAY_FIELDS_PREFIX": "", \
    "OUTPUT": peaks_intersection_path})
 
    # Remove layers
    project.removeMapLayer(peaks)
    project.removeMapLayer(iris)
 
    # Open the new intersected layer
    peaks_intersection = QgsVectorLayer(peaks_intersection_path, 'Peaks', "ogr")
    project.addMapLayer(peaks_intersection)
 
    # Register layer
    myIntersection = project.mapLayersByName('Peaks')[0]
 
# Run function with delay
QTimer.singleShot(200, myIntersection)

Other params here!